Gaussian Approximations for Maxima of Random Vectors under $(2+\iota )$-th Moments

We derive a Gaussian approximation result for the maximum of a sum of random vectors under $(2+\iota )$-th moments. Our main theorem is abstract and nonasymptotic, and can be applied to a variety of statistical learning problems. The proof uses the Lindeberg telescopic sum device along with some other newly developed technical results.